Infrared Behavior of Interacting Bosons at Zero Temperature

We exploit the symmetries associated with the stability of the superfluid phase to solve the long-standing problem of interacting bosons in the presence of a condensate at zero temperature. Implementation of these symmetries poses strong conditions on the renormalizations that heal the singularities of perturbation theory. The renormalized theory gives the following: For d . 3 the Bogoliubov quasiparticles as an exact result; for 1 , d # 3 a nontrivial solution with the exact exponent for the singular longitudinal correlation function, with phonons again as low-lying excitations